There is a long-standing prediction from neoclassical theory that strong contributions to the toroidal current should be driven by friction between trapped and passing particles when βpol exceeds in a tokamak. A number of neutral-beam heating experiments can now produce such parameters, and it is of interest to calculate the behaviour which should occur in this regime to determine the feasibility of using such a 'bootstrap' current as a steady-state tokamak current source. It is found that the neoclassical current should be large enough to reverse the external loop voltage for typical experimental parameters (ISX-B, in particular) in cases where the total current is fixed and to produce a detectable excess of total current above the pre-programmed (demand) value in cases where the loop voltage is regulated. Other manifestations of such a current should be either: a sharp rise in the central q-value (producing a cessation of internal m = 1 and m = 2 MHD activity), with an enhancement by two orders of magnitude of ion thermal conductivity (due to the formation of a hollow current density profile and a consequent drop in local values of the poloidal magnetic field in the central plasma region), or an enhanced tendency for disruption (arising from magnetic reconnection in hollow-profile equilibria). Since these gross manifestations are absent in a wide range of experiments on the Impurity Study Experiment (ISX-B), as reported earlier, the conclusion is that the neoclassical current, if present, can have a value no larger than 25% of its theoretically calculated value. Since the neoclassical particle (Ware) pinch is strongly related to the neoclassical current in the theory (Onsager reciprocity), the existence of the particle pinch is thus called into question.